Recall from our explanation of Algorithm  that \(k\)  is the number of subsets into
which we partition our original data, which in turn becomes the number of elements fed into our
private mean estimation algorithm, Algorithm .
This presents a trade-off for the user; when \(k\)  is large, the sensitivity of our aggregator decreases
(Line REF  of Algorithm REF ) and thus so does the
variance of the noise we need to add for privacy.
On the other hand, we assume that the mean and covariance estimates we get from the BLB
reasonably approximate the mean and covariance of the true sampling distribution of the parameters,
which is provably true only as \(n \rightarrow \infty \)  and
\(\frac{n}{k} \rightarrow \infty \)  (and our estimator is Hadamard differentiable) [1]}.
